Springer correspondence for exceptional Lie algebras and their duals in small characteristic

TL;DR

This paper explicitly describes the Springer correspondence for exceptional Lie algebras of types G2 and F4, and their duals, in small characteristics 2 and 3, addressing cases in bad characteristic.

Contribution

It provides explicit descriptions of the Springer correspondence for G2 and F4 Lie algebras in characteristics 2 and 3, which are previously less understood.

Findings

Explicit Springer correspondence for G2 and F4 in characteristics 2 and 3

Addresses cases in bad characteristic where previous descriptions were incomplete

Enhances understanding of representation theory in small characteristic

Abstract

We describe the Springer correspondence explicitly for exceptional Lie algebras of type $G_2$ and $F_4$ and their duals in bad characteristics, i.e. in characteristics 2 and 3.